Nodal solutions for the Choquard equation

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• 作者：Marco Ghimenti^a ; ^{marco.ghimenti@dma.unipi.it" class="auth_mail" title="E-mail the corresponding author} ; Jean Van Schaftingen^b ; ^{Jean.VanSchaftingen@uclouvain.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J91 ; 35J20
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：271
• 期：1
• 页码：107-135
• 全文大小：456 K

文摘

We consider the general Choquard equations where I_α$I_{\alpha }$ is a Riesz potential. We construct minimal action odd solutions for $p\in (\frac{N+\alpha }{N},\frac{N+\alpha }{N-2})$ and minimal action nodal solutions for $p\in (2,\frac{N+\alpha }{N-2})$. We introduce a new minimax principle for least action nodal solutions and we develop new concentration–compactness lemmas for sign-changing Palais–Smale sequences. The nonlinear Schrödinger equation, which is the nonlocal counterpart of the Choquard equation, does not have such solutions.